I notice the old fences around all have 2 horizontal rails for the
boards to attach to. I've also noticed that new specs often show 3
rails, without comment. I'm thinking that this might be due to the
fence boards being much thinner than they used to be.

I like to place my rails long side vertical, so I don't get excessive
sagging over time. But I'm thinking that unless I expect the fence to
see hard wind loads or other severe attacks (kicks, etc.), 2 rails
might be enough.

Any thoughts?